# Math Help - improper integral

1. ## improper integral

so, i need to either use tests or evaluation to decide whether this integral converges or diverges, but im not sure what to do!

integral from 0 to 1 of: 1/(t-sin(t))
i thought of doing a comparison to 1/t, but -sin(t) can take on both positive and negative values, so im not quite sure where to go

2. Originally Posted by mistykz
so, i need to either use tests or evaluation to decide whether this integral converges or diverges, but im not sure what to do!

integral from 0 to 1 of: 1/(t-sin(t))
i thought of doing a comparison to 1/t, but -sin(t) can take on both positive and negative values, so im not quite sure where to go
$\frac{1}{x-\sin x} \geq \frac{1}{x}$ on $[\epsilon,1]$ where $\epsilon >0$. And note $\int_0^1 \frac{dx}{x}$ diverges.